“You take your dice, repeat the same exercise by throwing them on the table, and you look at the result,” says Susana Guatelli, assistant professor of physics at the University of Wollongong in Australia.
By repeating the experiment of rolling the dice and recording the number of times the dice landed on each number, you can construct a “probability distribution”—a list that gives you the probability of the dice landing on each possible outcome.
For Monte Carlo simulations used in physics, “we repeat the same experiment many times,” says Guatelli. “When we use it to solve problems, we have to repeat the same experiment which, of course, is more difficult and complicated than rolling the dice.”
Like the universe itself, the Monte Carlo simulation is governed by randomness and chance. This makes them well suited for modeling natural systems. “Monte Carlo simulations are basically our way of simulating nature,” says Benjamin Nachman, a scientist at the US Department of Energy’s Lawrence Berkeley National Laboratory.
Illustration by Sandbox Studio, Chicago with Ariel Davis
Particle physicists use Monte Carlo simulations to design new experiments, to plan the construction of equipment, and to predict how that equipment will perform. After the researchers ran their experiments, they used Monte Carlo simulations to design their analyses, simulating both physical processes predicted by the Standard Model of particle physics and hypothetical processes beyond the Standard Model to understand what they might look like if they occurred.
One of the reasons Monte Carlo simulations are so useful is that they are now more accurate than they were in the past.
“We in high energy physics rely on Monte Carlo simulations for almost everything, and this is actually a relatively recent development,” says Kevin Pedro, associate scientist at Fermi National Accelerator Laboratory. “In previous generations of experiments, Monte Carlo instruments were much less accurate, so people didn’t trust them as much…but in the 1990s and 2000s, there was a lot of work to improve accuracy.”
Nachmann says the work has paid off. “The simulations are so good now that if you have a full simulated event, say, a collision at the Large Hadron Collider, and you show[the data]to an expert … most people won’t be able to tell you which one is real or which one is fake,” says Nachman. . “The Higgs boson (when it was) probably would not have been discovered without the level of accurate simulation we have.”
In the past decade or so, Monte Carlo simulations have become more powerful thanks to the support of machine learning.
MC simulation gets an ML boost
Monte Carlo simulations allow researchers to analyze events related to some independent variable, such as time or energy.
“One of the defining features of physical processes, or any other processes, is that there are different processes occurring on different time, energy, or length scales,” says Nachman. “The idea is that we have (some) particles — or whatever the basic unit of an object is — inside some simulation. We track these particles as they evolve through time or energy or whatever independent quantity is involved.”
The end result is a mathematical simulation of experimental data that closely resembles the real thing. “We want to be able to simulate some sets of data, and they need to look as similar as possible to data that we might see in some experiment,” Nachman says.
But this method of Monte Carlo simulation also has its limitations. “Although it’s very accurate, it’s kind of slow,” says Pedro.
For researchers, it is always an open question whether they can simulate enough individual events within the process they want to model so that the final simulation has the same statistical power as the real experimental data.
“And this is where AI comes in,” says Pedro.
In collider experiments, for example, the simulations are slow because of all the details that go into each implementation. The particles traverse the detector, and the researchers simulate their interaction with the detector material. However, any movement by a particle can cause a change in both the detector material and the type of reaction that takes place.
This means that not only the inputs but the actual calculations required by the simulation change with each computational step. Every particle wants to do something different, and this complexity is a challenge for modern computers to simulate.
“But if you just take (the end results) … the idea is that you can train some kind of AI algorithm that will very accurately reproduce that distribution,” says Pedro. “And it will do so (in a way that is easily) accelerated in modern computing architecture.”
In other words, the researchers are speeding up slow particle detector simulations by replacing part or all of them with machine learning models. They train these models on data from real detector experiments, or even with models trained on data from previous simulations. This framework is also applicable to many other areas of particle physics, and can improve not only simulation speed but also simulation accuracy.
“The basic idea is (always) a bit the same: there are some very computationally intensive tasks that you can approximate to a very good degree of accuracy with an AI algorithm if you are careful enough,” says Pedro.
Need a better ML model? Do it yourself.
Of course, just as Monte Carlo methods have their limits, so do the machine learning models that physicists use to speed them up. Partly because many machine learning approaches come from industry research, the datasets are very different, and arguably less complex.
“In industry AI research, they tend to look at text, images and videos,” says Pedro.
Human-generated data formats usually come with simple and regular structures. A sentence is a sequence of words. An image is a grid of pixels. Video is a series of pixel grids.
“The data we have in particle physics is regular in its own way, but … the relationships between the pieces of data are more complex,” says Pedro. “And a lot of times, that’s almost the entire problem — just trying to get existing AI to work on our data efficiently and in a way that makes sense.”
As a result, researchers such as Pedro sometimes find themselves taking AI and machine learning methods from industry and pushing these methods to limits beyond even traditional computer science research in terms of the scale or complexity of the problems they can tackle.
Pedro cited some examples of this from different areas of physics research, including a 2021 paper. In it, a group of high-energy physicists working on simulating jets of particles developed a new version of a machine learning model known as a generative adversarial network, or GAN. The researchers claimed that pre-existing GANs were “unsuitable for physics applications,” he says.
By making small modifications to these models, they were able to develop a new GAN that they say delivers improved quantitative results across each measure.
But while there are many benefits to integrating AI methods with physics applications, physicists also face a new set of challenges in dealing with the black box nature of machine learning algorithms themselves.
Machine learning algorithms are often good at building internal models that generate correct answers, but bad at explaining consistently what those models are, or why they are so confident in their results. AI researchers in both industry and science are still working to define the full scope of this “explainability” problem, although some argue that it is a particularly pressing topic for scientific applications.
“Because we’re not just trying to sell a product, right?” Pedro says. We are actually trying to learn something about the universe.
“You could have an algorithm that, inside of it, can learn a bunch of physics and then give you an answer, but that doesn’t really satisfy us as scientists because we want to learn physics too,” he says. “How do you get an algorithm to tell you what it has learned in a way that you can understand? This is also still a very open question.”